L/O/G/Owww.themegallery.com

A MEM-based Analysis of Volatility Spillovers in European Financial

Markets

Lena Golubovskaja

NUI Maynooth

FMC2/MACSI Colloquium

Introduction

Theoretical Developments

The MEM Models

Empirical Results4

1

2

3

Contents

• Financial volatility has been extensively investigated for more than twenty-five years

• Financial integration => cross-country transmission mechanisms

• Strong empirical regularities about GARCH models

Analysis of Volatility

Channels of Financial Contagion

Problems in a foreign bank subsidiary

Spillover to the parent

bank

Spillover to other countries where the parent banks and

other banks in home country have subsidiaries or engage in direct lending

to the private sector

Liquidity risk

Credit risk

Liquidity problems

Solvency problems

Spillover to other banks

in home country

Spillover to home banks with exposure to the affected subsidiary

Source: Árvai, Driessen, and Ötker-Robe (2009)

Chou, Wu, and Yung (2010)

DJIA

SP500

NAS100

DAX30

FTSE100

CAC40

DJIA

SP500

NAS100

DAX30

FTSE100

CAC40

DJIA

SP500

NAS100

DAX30

FTSE100

CAC40

A: Entire Period B: Pre-subprime,

2001/02 – 2007/06

C: Post-subprime

2007/07 – 2010/01

The relationships between the U.S. and European Stock Price Ranges

?

Whether volatility spillover effect exist between the European markets?

1

2

3

Do we have a symmetric or assymetric volatility mechanism among the markets?

Who is the main volatility transmitter during the subprime mortgage crisis?

Hypothesis

• Modelling non-negative time series– A lot of information available in financial

markets is positive valued: ultra-high frequency data (within a time interval: range, volume, number of trades, number of buys/sells, durations) daily volatility estimators (realized volatility, daily range, absolute returns)

– Time series exhibit persistence: GARCH–type models

Why Multiplicative Error Models?

Germany: Daily Range, 1991-2011

Autocorrelation 0.737

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20110.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Range-based Volatility

Parkinson (1980) showed that that the range is an unbiased estimator of the volatility parameter in a diffusion process. The intuition behind his finding is that the price range of intraday gives more information regarding the future volatility than two arbitrary points in this series (the closing prices).

Are These Days the Same?

Can we use this information to measure volatility better? Can we use this information to measure volatility better?

Volatility Proxy

• The daily range

)log()log( ,, lowthightt PPhl

• Theoretical relative efficiency gain 2.5-5 (Parkinson, 1980)

• Directly observable from the data

• It is well approximated as Gaussian

• Robust to the microstructure noise (Brandt and Diebold, 2006)

22 ))2log(4/( dailyrangeE

MEM

• Extension of GARCH approach to modelling the expected value of processes with positive support (Engle, 2002; Engle and Gallo, 2006)

• Autoregressive Conditional Duration is a special case

• Ease of estimation

• Possibility of expanding the information set

The Base Model

Assumptions• a non-negative univariate process• the information about the process up to time t-1• MEM for is specified as

• is a nonnegative predictable process, depending on a vector of unknown parameters θ

• is a conditionally stochastic i.i.d. process, with density having non-negative support, mean 1 and unknown variance

thl

1tI

thltttt Ihl 1

t

).,1(~ 21 DI tt

t

A Gamma Assumption for t

With and

/1)( 1 tt IV

)./1,(..~1 GammadiiI tt

11 tt I

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Gamma(4,1/4)

Chi-square

Gamma(2,1/2)

Exponential

=> )/,(~1 ttt GammaIhl

Range Density

0.00 0.01 0.02 0.03 0.04 0.05 0.06

0

25

50

75

100

125

150

175

0.00 0.01 0.02 0.03 0.04 0.05

0

25

50

75

100

125

150

175

France

The Netherlands

The specification of t

• Base(1,1) specification

1,1,, tiitiiiti hl

• Extended specification

1,01,1,,1,1,,

titiitjji

jitiitiiiti hlrIdhlhl

1, tir

0,0

0,10

1,

1,

1,ti

ti

ti rif

rifrI

- the return of stock i at time t-1.

- a dummy variable to test the leverage effect.

Estimation

thl

)/(lnln)1()(lnlnln tttttt hlhlLl

• The contribution of to the log likelihood function is

Gamma GED

• A useful relationship is between the Gamma distribution and the Generalized Error Distribution (GED):

• Thus the conditional density of hlt has a correspondence in a conditional density of hlt

where

).,,0(~)/,(~ 11 tttttt GEDHalfIhlGammaIhl

ttt vhl

).1,0(~1 NormalHalfIv tt

Cross-autocorrelation matricesΥ0 hlFRA,t hlGER,t hlNETH,t hlSPA,t

hlFRA,t 1.000

hlGER,t 0.812 1.000

hlNETH,t 0.843 0.847 1.000

hlSPA,t 0.793 0.723 0.754 1.000

Υ1 hlFRA,t-1 hlGER,t-1 hlNETH,t-1 hlSPA,t-1

hlFRA,t 0.607 0.601 0.604 0.545

hlGER,t 0.597 0.737 0.660 0.545

hlNETH,t 0.599 0.671 0.695 0.552

hlSPA,t 0.559 0.564 0.564 0.625

Estimation Results

t-stats

Forecasting Performance

France Germany

SpainNetherlands

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

18/0

7/20

07

25/0

7/20

07

01/0

8/20

07

08/0

8/20

07

15/0

8/20

07

22/0

8/20

07

29/0

8/20

07

05/0

9/20

07

12/0

9/20

07

19/0

9/20

07

26/0

9/20

07

03/1

0/20

07

10/1

0/20

07

17/1

0/20

07

24/1

0/20

07

31/1

0/20

07

07/1

1/20

07

14/1

1/20

07

Forecast

Actual

0

0.01

0.02

0.03

0.04

0.05

0.06

18/0

7/20

07

25/0

7/20

07

01/0

8/20

07

08/0

8/20

07

15/0

8/20

07

22/0

8/20

07

29/0

8/20

07

05/0

9/20

07

12/0

9/20

07

19/0

9/20

07

26/0

9/20

07

03/1

0/20

07

10/1

0/20

07

17/1

0/20

07

24/1

0/20

07

31/1

0/20

07

07/1

1/20

07

14/1

1/20

07

Forecast

Actual

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

18/0

7/20

07

25/0

7/20

07

01/0

8/20

07

08/0

8/20

07

15/0

8/20

07

22/0

8/20

07

29/0

8/20

07

05/0

9/20

07

12/0

9/20

07

19/0

9/20

07

26/0

9/20

07

03/1

0/20

07

10/1

0/20

07

17/1

0/20

07

24/1

0/20

07

31/1

0/20

07

07/1

1/20

07

14/1

1/20

07

Forecast

Actual

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

18/0

7/2

007

25/0

7/2

007

01/0

8/2

007

08/0

8/2

007

15/0

8/2

007

22/0

8/2

007

29/0

8/2

007

05/0

9/2

007

12/0

9/2

007

19/0

9/2

007

26/0

9/2

007

03/1

0/2

007

10/1

0/2

007

17/1

0/2

007

24/1

0/2

007

31/1

0/2

007

07/1

1/2

007

14/1

1/2

007

Forecast

Actual

Forecasting

Market France Germany Netherlands Spain

MEM MA(65) MEM MA(65) MEM MA(65) MEM MA(65)

ME -0.0006 -0.0008 -0.0004 -0.0007 -0.0004 -0.0011 -0.0001 -0.0010

MAE 0.0020 0.0023 0.0019 0.0021 0.0016 0.0021 0.0025 0.0029

RMSE 0.0027 0.0029 0.0025 0.0026 0.0021 0.0026 0.0033 0.0037

MSE 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001

Theil’s U

0.7581 0.8036 0.7864 0.8027 0.8059 0.9802 0.7499 0.8309

Summing Up

• We find evidence of dependence across European markets over full sample and over post-subprime

• MEM is a flexible class of models to estimate conditional expectations of non-negative processes

• Captures a wide range of features suggested by data structure

• Challenge: handle a large panel of data

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Thank You!